A recurring important problem associated with production and evaluation of satellite earth terminals is the measurement, i.e. estimation, of the terminal figure of merit, G/T. One approach to determining G/T requires the separate evaluation of the terminal gain (G) and terminal system noise temperature (T), including sky noise, at a common reference point, usually the low noise amplifier (LNA) input, from which the ratio G/T may be computed. Although system noise temperature may be accurately estimated using hot/cold load measurements, accurate measurement of antenna gain using range measurements is considerably hampered by reflections, near-field effects, and the need for either a precisely characterized standard gain reference antenna or a calibrated RF signal source.
A more widely used approach for evaluating terminal G/T relies upon using extraterrestrial radio sources such as the sun, moon, and strong radio stars, e.g., Cassiopeia-A, Cygnus-A and Taurus-A, and inferring the G/T ratio from Y-factor measurements. Antenna gain can then be computed, if desired, from this ratio if system noise temperature is known.
Y-factor is typically obtained using a two step measurement process illustrated in FIG. 1. The terminal antenna 11 is first pointed at "cold sky" 12 and a measurement P.sub.1 of the received power is obtained. The power level P.sub.1 measured by aiming the antenna 11 at cold sky 12 includes terminal thermal noise and sky noise. A second power level P.sub.2 is then measured by aiming the terminal antenna 11 at radio source 13. Power level P.sub.2 includes terminal thermal noise, sky noise, and source noise.
These power levels can also be represented in terms of equivalent noise temperatures via the relationship EQU P=kTB (1)
where P is noise power, k is Boltzmann's constant, T is noise temperature, and B is the measurement bandwidth. The figure of merit (G/T) of the satellite earth terminal may be derived from Y factor measurements, as follows. The Y factor is defined as: ##EQU1## where T=terminal noise temperature plus sky noise temperature, and
.DELTA.T=noise temperature of the extraterrestrial radio source.
The noise temperature of the source can be expressed as EQU .DELTA.T=.GAMMA.SA/K (3)
where S is the flux density (W/m.sup.2 /Hz) of the source, A is the effective aperture area of the antenna and .GAMMA. is a constant accounting for effects such as atmospheric transmission, system bandwidth, polarization, etc. Effective aperture can be related to antenna gain and operating wavelength, .lambda., by EQU A=.nu..sup.2 G/4.pi. (4)
Thus EQU .DELTA.T=.GAMMA.S.lambda..sup.2 G/4.pi.k (5)
Substituting equation (5) into equation (2) and solving for G/T yields the desired connecting relationship between Y-factor and G/T, i.e. ##EQU2##
Now, although G/T is generally defineable by measurement determination, from a practical standpoint antenna aperture size will determine which extraterrestrial radio sources can be used for estimating G/T. For example, small-aperture, low-gain antennas cannot use radio star sources since the resulting measured Y-factor values are small relative to Y-factor measurement errors. These small-aperture terminals must use the sun or the moon as a radio source in order to achieve suitably large Y-factor values. When using the moon or the sun as a radio source, one must account for the following factors: (1) change in distance to the source with time; (2) changes in apparent angular extent of the source with time (this implies that the factor that accounts for the finite angular extent must be adjusted accordingly); and (3) changes in source flux density with time. These changes occur on a monthly (lunar cycle) basis for the moon source and on an annual basis for the sun source, except that solar flux density is a random variable and its value at a given time must be obtained from the National Bureau of Standards.
On the other hand, terminals employing large aperture antennas are well-suited for use with radio star sources since their large antenna gains yield large measured Y-factor values (several dB). As is the case for small antennas used with the sun or moon, the angular extent of the radio star source must be taken into account since the angular extent of the radio star may not be negligible with respect to the antenna beamwidth.
Between these two sizes are medium-aperture antennas which, unfortunately, are not well suited for use with the sun or moon as a radio source, since the medium aperture beamwidth is small compared to the angular extent of the sun or moon (approximately 0.5.degree.). The resulting Y-factor measurements are not useful since the radiated flux density of the sun and the moon will vary depending upon which portion of the surface is being illuminated, i.e., examined, by the antenna. Furthermore, significant source flux may be captured by the antenna's side lobe structure. On the other hand, medium-aperture antennas yield small measured Y-factor values (tenths of dB) when a radio star is used as the extraterrestrial source. The result is that small Y-factor measurement errors significantly degrade the accuracy of the G/T estimate since the nominal Y-factor is small. The fact that G/T estimate errors increase when Y-factors become smaller and the measurement error remains the same is explained below.
From equation (6) it can be shown that ##EQU3## so that ##EQU4## It is clear that Y-factor measurement errors in dB, (.DELTA.Y).sub.dB, are magnified by the factor ##EQU5## It is obvious that smaller nominal Y-factors (dB) imply larger G/T errors (dB) even though measurement error (.DELTA.Y).sub.dB remains constant. The value of the Y-factor error magnification factor m is plotted versus nominal Y-factor in FIG. 2.
The characteristic plotted in FIG. 2 emphasizes constraints that affect an estimation of G/T for medium aperture antennas, i.e. (1) the sun and moon cannot be used as a radio source; (2) small nominal Y-factors result when radio stars are used as sources; and (3) Y-factor measurement error is fixed regardless of nominal Y-factor.
This G/T estimation problem is similar to the communication problem of detecting a weak signal embedded in additive noise. A single sample of signal-plus-noise may not permit the desired detection performance due to insufficient per-sample signal-to-noise ratio, SNR.sub.s. However, the problem may be remedied by utilizing multiple (N) samples to determine whether the signal is present. The resulting performance is the same as if the effective SNR were .sqroot.N SNR.sub.s. This is because the signal samples are coherent and the noise samples are incoherent. The same improvement can be obtained in estimating Y-factor since measurement errors are independent from one measurement to the next. Thus, one reasonable approach is to make multiple Y-factor measurements and compute the average Y-factor. This has the effect of reducing the effective measurement error by the factor .sqroot.N.
In an ideal situation, one would have perfect knowledge of antenna location and star source position versus time, as well as the capability to point the antenna to a specified position without error. In this case, one would simply track the radio source perfectly and integrate the output of the power detection device; error due to Y-factor measurement could be made arbitrarily small by integrating over a sufficiently long interval.
In practice, of course, perfect tracking of the source is not possible. Instead, multiple Y-factor measurements are typically made by having an operator locate the star within the antenna beamwidth and manually steer the beam to "peak up" the power meter reading. This process is repeated until the desired number of "peak" Y-factor measurements have been made. This is a time-consuming, labor-intensive, error-prone, potentially inaccurate process that depends upon the skill of the operator. Typically, the highest and lowest Y-factor measurements are discarded from the data set prior to computing the average Y-factor; this is done to eliminate what are assumed to be, but are not necessarily, possible "bad" measurements.